EXACT CONFIDENCE INTERVALS
FOR THE MEANS OF NORMAL DISTRIBUTIONS
Confidence interval of a mean ...
[edit] Confidence intervals
Most studies will only sample part of a population and then the result is used to interpret the null hypothesis in the context of the whole population.
Confidence intervals for other location estimators such as the median or mid-mean tend to be mathematically difficult or intractable. For these cases, confidence intervals can be obtained using the bootstrap.
Case Study
Heat flow meter data.
Confidence interval estimation provides a convenient alternative to significance testing in most situations. Consider the 2-tailed hypothesis of no difference between means.
90 % Confidence Interval for Mean Statistic:
lower bound = 7.59778
upper bound = 14.23857
> ...
Standard techniques are learning confidence intervals (e.g. error bars for neural networks) and general probability density estimation.
As Luk explains, it's probably simplest and best to calculate a 95% confidence interval. If it's small and roughly centers on zero, you can argue with confidence that any effect is too small to be of interest- that the null is approximately true.
 See also: Distribution, Variance, Standard Deviation, Normal distribution, Regression
  
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